SOLUTION: Plane travels 1,176 miles to Miami and back. Going there took 14 hours. The trip back took 28 hours. What was the planes airspeed and the windspeed?

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Question 552626: Plane travels 1,176 miles to Miami and back. Going there took 14 hours. The trip back took 28 hours. What was the planes airspeed and the windspeed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s = speed in still air
Let w = wind speed
+s+%2B+w+ = the speed for 14 hr trip ( with the wind )
+s+-+w+ = the the speed for 28 hr trip ( against the wind )
-------------
With the wind:
(1) +1176+=+%28+s+%2B+w+%29%2A14+
Against the wind:
(2) +1176+=+%28+s+-+w+%29%2A28+
--------------------
(1) +s+%2B+w+=+1176%2F14+
(1) +s+%2B+w+=+84+
and
(2) +s+-+w+=+1176%2F28+
(2) +s+-+w+=+42+
Add (1) and (2)
(1) +s+%2B+w+=+84+
(2) +s+-+w+=+42+
+2s+=+126+
+s+=+63+
and
(1) +s+%2B+w+=+84+
(1) +63+%2B+w+=+84+
(1) +w+=+21+
Plane's air speed is 63 mi/hr
Wind speed is 21 mi/hr
check:
(1) +1176+=+%28+63+%2B+21+%29%2A14+
(1) +1176+=+84%2A14+
(1) +1176+=+1176+
and
(2) +1176+=+%28+63+-+21+%29%2A28+
(2) +1176+=+42%2A28+
(2) +1176+=+1176+
OK